A Mathematical Model for Tumor Growth and Treatment Using Virotherapy
Session Title
Cancer and Biomedical Research
College
College of Arts and Sciences
Department
Mathematics
Abstract
We present a system of four nonlinear differential equations to model the use of virotherapy as a treatment for cancer. This model describes interactions among infected tumor cells, uninfected tumor cells, effector T-cells, and virions. Using various stability analysis techniques, we establish a necessary and sufficient treatment condition to ensure a globally stable cure state. We additionally show the existence of a cancer persistence state when this condition is violated and provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature. We conclude with a discussion on the biological implications of our results.
Honors Thesis Committee
Zach Abernathy, Ph.D.; Kristen Abernathy, Ph.D.; and Trent Kull, Ph.D.
Previously Presented/Performed?
SAEOPP McNair/SSS Scholars Research Conference, Atlanta, Georgia, June 2018; Fifth Annual Showcase of Undergraduate Research and Creative Endeavors (SOURCE), Winthrop University, April 2019
Grant Support?
Supported by a Ronald E. McNair Post-Baccalaureate Achievement Program grant from the U.S. Department of Education
Start Date
12-4-2019 1:00 PM
A Mathematical Model for Tumor Growth and Treatment Using Virotherapy
WEST 219
We present a system of four nonlinear differential equations to model the use of virotherapy as a treatment for cancer. This model describes interactions among infected tumor cells, uninfected tumor cells, effector T-cells, and virions. Using various stability analysis techniques, we establish a necessary and sufficient treatment condition to ensure a globally stable cure state. We additionally show the existence of a cancer persistence state when this condition is violated and provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature. We conclude with a discussion on the biological implications of our results.
